Heat and mass transfer characteristics of the self-similar boundary layer flows induced by continuous surfaces stretched with rapidly decreasing power law velocities Uw proportional to xm, m<-1 are considered for mixed convection flow. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, dimensionless injection/suction velocity f(w), and the mixed convection parameter λ = s Gr/Re2 are studied. These parameters have great effects on velocity and temperature profiles, heat transfer coefficient, and skin friction coefficient at the moving surface. Results show that similarity solutions exist only when the condition n=2m-1 is satisfied. Critical values of λ, Nu/Re0.5 and Cf Re0.5 are obtained for predominate natural convection for different Prandtl numbers at m=-2, -6 and n=-5, and -13 respectively. Results also show that the effect of buoyancy is more significant for weak than for strong suction. Furthermore, critical Prandtl numbers where fw profiles have minimums are obtained for m=-2 and -6. Finally, critical values of λ, Cf Re0.5 are also obtained for predominate natural convection for both m=-2 and -6.